Part A Prove the following theorem using either regular or strong induction. Theorem: Suppose that n ≥ 2 people are at a gathering. Every person shakes hands with every other person, but not themselves. Then, the number of total handshakes which occur is

Q: Find the given inverse transform: L-1 1 s3+5s.

A:

Q: 5. Show the congruence axiom C3 for II (don't assume the field is Pythagorean)

A: To prove: The congruence axiom C3 for ΠF.

Q: Prove that (1, 2) (1,(1), 2, 3).

A: We know, if A and B are two sets then, A is subset of B  if every element in A is also in B.

Q: -3 -1 -2 Use the Gauss-Jordan method to find the inverse of A = 7 or 3 2 -4. show that A is not…

A: We will use Gauess-Jorden  method to find the inverse of matrix. In this method we put the the given…

Q: Prove Taylor's theorem.

A: The objective is to prove Taylor's theorem. According to Taylor's theorem we have, If fx be a…

Q: Show by universal generalization (twice-applied) ((CC-A) AB) U (DNB)) = (BN((C-AJUD)).

A:

Q: 19. Is Q[x]/(x² – 6x + 6) a field? Why?

A:

Q: 2. Show that Q√3 = {a+b√3|a, b = Q} is a field by verifying the field axioms one by one.

A:

Q: (a) The matriz 1 3 -1 0 5 3 0 2 is invertible. Find A- by any method you know.

A:

Q: Let A = [-6, 8) U [10, ∞). Ext(A) = ?

A: The given set .The aim is to find the exterior of the set .

Q: Could you derive the equation from this for βi that is used by the Newton algorithm

A:

Q: Find the function f(x) that has Fourier transform (k) = (1+k4)-1.

A: Here we have to find out  .Now from definition of inverse fourier transform , to evaluate this…

Q: Find the given inverse transform L .((무) + (+) - (주) } { s2 S-2 O t+1+e2t O t– 1– e2t O t+ e2t…

A: Given that L−11s2−1s+1s−2. We have to find the inverse Laplace transform. Use formula L−1n!sn+1=tn…

Q: 3. There are three distinct cube roots of any nonzero real number c. (a) Set up an algebraic…

A: Sol:- (a) To find the three distinct cube roots of a nonzero real number c, we can set up the…